In [1]}, we give some equivalent conditions about \(\mathbb {G}\) -regular hypersurface inside the Carnot groups of step 2 (see Theorem 5.7 in [1]}). In this section we give another one. More precisely, we show that if a continuous map \(\phi :\mathcal {O}\subset \mathbb {R}^{m+n-1}\rightarrow \mathbb {R}\)  is locally little \(1/2 \) -Hölder continuous along the vertical components, then \(\phi \)  is a distributional solution in an open set \(\mathcal {O}\)  of the non linear first order system \((\ref {sistema})\)  if and only if \(\hat{\phi }: \hat{\mathcal {O}}\rightarrow  is uniformly intrinsic differentiable in \) O\( and consequently its graph is a \) G\(-regular hypersurface. The main equivalence result is contained in Theorem \ref {CharacterizationRegularSurfaces}.\) In order to state the equivalence result we have to be precise about the meaning of being a solution of (REF ). To this aim we recall a notion of generalized solutions of systems of this kind. These generalized solutions, denoted
broad* solutions were introduced and studied for the system (REF ) inside Heisenberg groups in [3]}, [4]}. For a more complete bibliography we refer to the bibliography in [3]}. Our strategy will be to prove that each continuous distributional solution of the system (REF ) is a broad* solution and vice versa (see Proposition REF ).
